Thank you Noah for this comprehensible crash course on the deepest issues of Quantum Mechanics!!! These videos will last as a reference for me from now on.... Thanks!!!!
I can say exactly the same! And I really appreciate the lack of mystical mistery some people in TH-cam want to link with quantum mechanics... I love the way you explain entanglement and measurement!!!! And I envy your concept clarity... Thanks!!!!
Thank you Noah for such a wonderful video. Even though it's a monologue, it felt like you were in the room and you were simply doodling stuff and explaining things. More power to you for making such amazing content available.
Very pretty physics of spin-1/2 (spin) measurement in this video! Quantum information theorists have another way to understand quantum mechanics (QM) that gives a “bare bones” understanding of what’s going on with spin (misses the beautiful physics shown in this video), but it provides a reason for the spin outcomes we observe. We explain this in our book, "Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit" Oxford UP (2024) and I’ll summarize it here. According to Einstein, special relativity (SR) is a "principle theory," i.e., a theory whose formalism follows from an empirically discovered fact. For SR that empirically discovered fact is the light postulate - everyone measures the same value for the speed of light c, regardless of their relative motions. Since c is a constant of Nature according to Maxwell's electromagnetism, the relativity principle (the laws of physics are the same in all inertial reference frames) says it must be the same in all inertial reference frames. And, since inertial reference frames are related by uniform relative motions (boosts), the relativity principle tells us the light postulate must obtain, whence the Lorentz transformations of SR. Likewise, quantum information theorists have rendered QM a principle theory and its empirically discovered fact is called Information Invariance & Continuity (Brukner & Zeilinger, 2009). In more physical terms, Information Invariance & Continuity entails that everyone measures the same value for Planck's constant h, regardless of their relative spatial orientations or locations (let me call that the "Planck postulate"). Since h is a constant of Nature according to Planck's radiation law, the relativity principle says it must be the same in all inertial reference frames. And, since inertial reference frames are related by relative orientations or locations in space (rotations or translations), the relativity principle tells us the Planck postulate must obtain, whence the finite-dimensional Hilbert space of QM. Quantum superposition is one consequence of the Planck postulate and here is how it makes perfect sense using spin as shown in this video. Suppose you send a vertical spin up electron to Stern-Gerlach (SG) magnets oriented at 60 deg relative to the vertical. Since spin is a form of angular momentum, classical mechanics says the amount of the vertical +1 angular momentum that you should measure at 60 deg is +1*cos(60) = 1/2 (in units of hbar/2). But the SG measurement of electron spin constitutes a measurement of h (Weinberg, 2017), so everyone has to get the same +/- 1 for a spin measurement in any SG spatial orientation, which means you can't get what you expect from common sense classical mechanics. Instead, QM says the measurement of a vertical spin up electron at 60 deg will produce +1 with a probability of 0.75 and it will produce -1 with a probability of 0.25, so the average is (+1 + 1 + 1 - 1)/4 = 1/2. In other words, QM says you get the common sense classical result on 'average only' because of the observer-independence of h. Give up your dynamical bias for QM (just as is done for SR) and the physics of spin makes perfect sense. And if you explore the Bell states for spin-entangled pairs using this approach, you find it solves the mystery of entanglement without violating locality (as in Bohm’s pilot wave), statistical independence (as in superdeterminism or retrocausality), intersubjective agreement (as in QBism), or the uniqueness of experimental outcomes (as in Many Worlds).
I did follow the complete series and I loved it. As with all good things it is regrettable that it stops here! I thought: well, let me continue with the book of Sakurai and Napolitano that starts with promising to give the Stern-Gerlach experiment a central role. But some of the subjects treated by you seem to be missing. No decoherence, coherence, noise in the index!
Thanks for this series! While I knew about e.g. the spin group, and SU(2) being a double cover of SO(3), I had never really uh, taken much of a look at things like, how the spin evolves in a magnetic field, and how it fits together with overall particle motion (and I certainly wasn't familiar with the things like the classical derivations of e.g. the force on the magnetic moment in a changing magnetic field, etc. ). This taught me a fair bit. Thanks!
Noah is a fantastic educator, but if you want to go deeper on spin maths relations SU(2), etc go and check Richard behiel video on spin... And pause it every 30 seconds to understand the details... And If you want to go even deeper, go to eigenchris videos on spinors... Quaternions relativistic spacetime, etc.... Really understanding spin as Noah shows or others can take a lot of time and give also time to challenge your self learned concepts by reviewing this series after the whole mental trip....
Dear friend, go and find a good maxwell electrodinamics course that takes you from maxwell E and B to the easier and more real A and omega (vector potentials), and realize that B is an effect, a consequence of B and the real thing is A as the quantum Lamb effect experiments shows. B is something that's affected by materials frontiers and properties etc, And if you get to learn A you will inmediately understand how a electromagnetic wave is generated by an accelerating charge or changing current in the direction of such movement and how electromagnetic fields just expand from that initial point parallel to the movement direction... And if you really want to go deeper after understanding all of this, go and check geometric algebra formulation on maths and Physics.... The journey never ends... And by the way, what's an electriccharge? A clue is that it.s linked to rotations... But what it is? Probably nobody knows or can explain it
sad to see this series end! I was hoping an episode would cover how things change for spin-1 particles. I'm interested to know why rotating a spin-1 particle wouldn't introduce the phase change you showed with spin precession.
Thank you for this. It may interest you to know that though the silver atom has the spin of an electron, you cannot use this experiment to directly measure the spin on a free electron due to the uncertainty principle!
that was a great and very elegant video....IMO its your best so far. It tied together several different ideas that are in other videos in varying degrees. as a non-physicist, non-mathematician my overall impression is that Quantum Mechanics is definitely a thing but it needs an entirely new mathematics and an entirely new notation before it really makes any sense to anybody .... i'd say that you physicists have about 10% of quantum mechanics basics solved rationally and all the rest, about 90%, is suspended in a Hail Mary pass situation based on Dirac notation and impossible superpositions and impossible entanglements that are no longer fit for purpose and which inhibit any further progress in particle physics......there are just too many illogical anti-intuitive bizarreries in standard QM that chain the mind and embarrass the thinker into believing 3 ridiculous things before breakfast every single day........and fantasies are not the way to the stars. the next Einstein, when he is eventually born, will go right back to the beginning of QM and restate all the notation and math and revolutionize this "steam locomotive level QM" into something dazzling and coherent and otherworldly yet rational way.....just as Einstein supplanted Newton with his spacetime and relativity. But that all might be 200 years in the future....humanity turns out a Newton and an Einstein about once every 500 years.
Hey, thank you so much for uploading this series, it was wonderful. One question though, can you explain how the concept of spin(representing a wave function by 2 complex numbers) eventually leads to each orbital being able accomodate 2 electrons? An orbital is still just one state and the Pauli exclusion principle should only allow one electron in it.
6:30 Does it mean that if there will be NO variation of a magnetic field over Z in that device, the rotating charge will not experience any force at all?
Well, remember that there are two forces. There's the Lorentz force law, F = q v x B, and there's the dipole force law, F =∇ (μ · B). A charged particle with a charge q will still feel the Lorentz force q v x B. But if the particle has no net charge (q=0) like a silver atom, then the only force is ∇ (μ · B). Then, if the magnetic field B is constant, then YES, that particle will feel no force.
@@noahexplainsphysics Indeed. Thanks. One more question if I may: is it possible to create a linear fully homogeneous (at least in the Z direction) magnetic field in the lab?
@@andreylebedenko1260 I know that in the idealized case, the magnetic field inside a solenoid (a cylindrical coil of wire with a current running through it) will be constant and homogenous. This is a good approximation if the length of the cylinder is much longer than the radius. There are probably a large number of other ways to created a roughly homogenous magnetic field, but I don't know of them.
@@noahexplainsphysics I was under impression that the strength of the magnetic field is inversely proportional to the square of the distance from the source. Hence I struggle to imagine the device which would generate the field of equal strength in every given point of space regardless of the volume.
@@andreylebedenko1260 it is inversely proportional to linear distance, not its square. This did indeed lead to a constant magnetic field inside a cylindrical solenoid. Forces proportional to the square like gravity (or electrostatics) are constant and zero inside a hollow sphere of constant density (or charge density). Proofs for both cases use an argument from symmetry, where you can take an arbitrary point inside and divide the force felt there into tiny triangles/cones.
About to watch while cycling. Seeking to understand: Are atoms machines for practical purposes? Do atoms process signals or information? Are atoms elemental quantum computers? All of which are philosophy or theology questions implicit in bible, John "In the beginning was The Logos", numbers, geometry, language. Are atoms physical or incarnate mathematics?
Hi, Very informative !! There is a lack of 3D animation ...... The fact that the particles are entangled is understandable. How to unravel all this ?? :)) What if. Your reasoning and calculations, transfer not to particles, but to information ?? ------------------------------------------------------------------------------ Привет, Очень познавательно!! Не хватает 3D анимации...... То что частицы запутаны-это понятно. Как все это распутать?? :)) А что если. Ваши рассуждния и расчеты, перенести не на частицы, а на информацию??
12:47 “can only be up or down” if you look at the original experiment then you would see that that actually depends on the strength of the magnetic field. when the magnetic field was weak then it was actually spread normally.
Thank you Noah for this comprehensible crash course on the deepest issues of Quantum Mechanics!!! These videos will last as a reference for me from now on.... Thanks!!!!
I can say exactly the same! And I really appreciate the lack of mystical mistery some people in TH-cam want to link with quantum mechanics... I love the way you explain entanglement and measurement!!!! And I envy your concept clarity... Thanks!!!!
Great explanation. It is better than my Nobel Prize professor.
Sir you are a simply amazing physics educator... Absolutely crystal clear concepts & communication more importantly.
Great, lots of details that correct the other videos.
Thank you Noah for such a wonderful video. Even though it's a monologue, it felt like you were in the room and you were simply doodling stuff and explaining things. More power to you for making such amazing content available.
Your explanations are too good! I'm looking forward to more video on such ideas in quantum mechanics like decoherence.
Very pretty physics of spin-1/2 (spin) measurement in this video! Quantum information theorists have another way to understand quantum mechanics (QM) that gives a “bare bones” understanding of what’s going on with spin (misses the beautiful physics shown in this video), but it provides a reason for the spin outcomes we observe. We explain this in our book, "Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit" Oxford UP (2024) and I’ll summarize it here.
According to Einstein, special relativity (SR) is a "principle theory," i.e., a theory whose formalism follows from an empirically discovered fact. For SR that empirically discovered fact is the light postulate - everyone measures the same value for the speed of light c, regardless of their relative motions. Since c is a constant of Nature according to Maxwell's electromagnetism, the relativity principle (the laws of physics are the same in all inertial reference frames) says it must be the same in all inertial reference frames. And, since inertial reference frames are related by uniform relative motions (boosts), the relativity principle tells us the light postulate must obtain, whence the Lorentz transformations of SR.
Likewise, quantum information theorists have rendered QM a principle theory and its empirically discovered fact is called Information Invariance & Continuity (Brukner & Zeilinger, 2009). In more physical terms, Information Invariance & Continuity entails that everyone measures the same value for Planck's constant h, regardless of their relative spatial orientations or locations (let me call that the "Planck postulate"). Since h is a constant of Nature according to Planck's radiation law, the relativity principle says it must be the same in all inertial reference frames. And, since inertial reference frames are related by relative orientations or locations in space (rotations or translations), the relativity principle tells us the Planck postulate must obtain, whence the finite-dimensional Hilbert space of QM.
Quantum superposition is one consequence of the Planck postulate and here is how it makes perfect sense using spin as shown in this video.
Suppose you send a vertical spin up electron to Stern-Gerlach (SG) magnets oriented at 60 deg relative to the vertical. Since spin is a form of angular momentum, classical mechanics says the amount of the vertical +1 angular momentum that you should measure at 60 deg is +1*cos(60) = 1/2 (in units of hbar/2). But the SG measurement of electron spin constitutes a measurement of h (Weinberg, 2017), so everyone has to get the same +/- 1 for a spin measurement in any SG spatial orientation, which means you can't get what you expect from common sense classical mechanics. Instead, QM says the measurement of a vertical spin up electron at 60 deg will produce +1 with a probability of 0.75 and it will produce -1 with a probability of 0.25, so the average is (+1 + 1 + 1 - 1)/4 = 1/2. In other words, QM says you get the common sense classical result on 'average only' because of the observer-independence of h.
Give up your dynamical bias for QM (just as is done for SR) and the physics of spin makes perfect sense. And if you explore the Bell states for spin-entangled pairs using this approach, you find it solves the mystery of entanglement without violating locality (as in Bohm’s pilot wave), statistical independence (as in superdeterminism or retrocausality), intersubjective agreement (as in QBism), or the uniqueness of experimental outcomes (as in Many Worlds).
I did follow the complete series and I loved it. As with all good things it is regrettable that it stops here! I thought: well, let me continue with the book of Sakurai and Napolitano that starts with promising to give the Stern-Gerlach experiment a central role. But some of the subjects treated by you seem to be missing. No decoherence, coherence, noise in the index!
Thanks for this series! While I knew about e.g. the spin group, and SU(2) being a double cover of SO(3), I had never really uh, taken much of a look at things like, how the spin evolves in a magnetic field, and how it fits together with overall particle motion (and I certainly wasn't familiar with the things like the classical derivations of e.g. the force on the magnetic moment in a changing magnetic field, etc. ).
This taught me a fair bit. Thanks!
Did you come back after the SoME1 vid, XD
@@shunleung3734 the SoME1 video was how I found the channel, so if that’s what you are asking, yes.
Noah is a fantastic educator, but if you want to go deeper on spin maths relations SU(2), etc go and check Richard behiel video on spin... And pause it every 30 seconds to understand the details... And If you want to go even deeper, go to eigenchris videos on spinors... Quaternions relativistic spacetime, etc.... Really understanding spin as Noah shows or others can take a lot of time and give also time to challenge your self learned concepts by reviewing this series after the whole mental trip....
Dear friend, go and find a good maxwell electrodinamics course that takes you from maxwell E and B to the easier and more real A and omega (vector potentials), and realize that B is an effect, a consequence of B and the real thing is A as the quantum Lamb effect experiments shows. B is something that's affected by materials frontiers and properties etc, And if you get to learn A you will inmediately understand how a electromagnetic wave is generated by an accelerating charge or changing current in the direction of such movement and how electromagnetic fields just expand from that initial point parallel to the movement direction... And if you really want to go deeper after understanding all of this, go and check geometric algebra formulation on maths and Physics.... The journey never ends... And by the way, what's an electriccharge? A clue is that it.s linked to rotations... But what it is? Probably nobody knows or can explain it
Very good inside on quantum measurements. Many many thanks!
sad to see this series end! I was hoping an episode would cover how things change for spin-1 particles. I'm interested to know why rotating a spin-1 particle wouldn't introduce the phase change you showed with spin precession.
excellent channel
Wow great video. Thank you for your time
This is very helpful, thank you.
Thank you for this. It may interest you to know that though the silver atom has the spin of an electron, you cannot use this experiment to directly measure the spin on a free electron due to the uncertainty principle!
that was a great and very elegant video....IMO its your best so far. It tied together several different ideas that are in other videos in varying degrees.
as a non-physicist, non-mathematician my overall impression is that Quantum Mechanics is definitely a thing but it needs an entirely new mathematics and an entirely new notation before it really makes any sense to anybody .... i'd say that you physicists have about 10% of quantum mechanics basics solved rationally and all the rest, about 90%, is suspended in a Hail Mary pass situation based on Dirac notation and impossible superpositions and impossible entanglements that are no longer fit for purpose and which inhibit any further progress in particle physics......there are just too many illogical anti-intuitive bizarreries in standard QM that chain the mind and embarrass the thinker into believing 3 ridiculous things before breakfast every single day........and fantasies are not the way to the stars.
the next Einstein, when he is eventually born, will go right back to the beginning of QM and restate all the notation and math and revolutionize this "steam locomotive level QM" into something dazzling and coherent and otherworldly yet rational way.....just as Einstein supplanted Newton with his spacetime and relativity. But that all might be 200 years in the future....humanity turns out a Newton and an Einstein about once every 500 years.
Hey, thank you so much for uploading this series, it was wonderful.
One question though, can you explain how the concept of spin(representing a wave function by 2 complex numbers) eventually leads to each orbital being able accomodate 2 electrons? An orbital is still just one state and the Pauli exclusion principle should only allow one electron in it.
This is a great lecture! ty
Thank you, i much more beleive my idea (Thumbnail )
6:30 Does it mean that if there will be NO variation of a magnetic field over Z in that device, the rotating charge will not experience any force at all?
Well, remember that there are two forces. There's the Lorentz force law, F = q v x B, and there's the dipole force law, F =∇
(μ · B). A charged particle with a charge q will still feel the Lorentz force q v x B. But if the particle has no net charge (q=0) like a silver atom, then the only force is ∇
(μ · B). Then, if the magnetic field B is constant, then YES, that particle will feel no force.
@@noahexplainsphysics Indeed. Thanks. One more question if I may: is it possible to create a linear fully homogeneous (at least in the Z direction) magnetic field in the lab?
@@andreylebedenko1260 I know that in the idealized case, the magnetic field inside a solenoid (a cylindrical coil of wire with a current running through it) will be constant and homogenous. This is a good approximation if the length of the cylinder is much longer than the radius. There are probably a large number of other ways to created a roughly homogenous magnetic field, but I don't know of them.
@@noahexplainsphysics I was under impression that the strength of the magnetic field is inversely proportional to the square of the distance from the source. Hence I struggle to imagine the device which would generate the field of equal strength in every given point of space regardless of the volume.
@@andreylebedenko1260 it is inversely proportional to linear distance, not its square. This did indeed lead to a constant magnetic field inside a cylindrical solenoid.
Forces proportional to the square like gravity (or electrostatics) are constant and zero inside a hollow sphere of constant density (or charge density).
Proofs for both cases use an argument from symmetry, where you can take an arbitrary point inside and divide the force felt there into tiny triangles/cones.
Make more videos
About to watch while cycling. Seeking to understand: Are atoms machines for practical purposes? Do atoms process signals or information? Are atoms elemental quantum computers? All of which are philosophy or theology questions implicit in bible, John "In the beginning was The Logos", numbers, geometry, language. Are atoms physical or incarnate mathematics?
❤
46:20 "Hilbert space isn't intimidating" Ha! Haaaaaaaaaa!
Hi,
Very informative !! There is a lack of 3D animation ......
The fact that the particles are entangled is understandable.
How to unravel all this ?? :))
What if. Your reasoning and calculations, transfer not to particles, but to information ??
------------------------------------------------------------------------------
Привет,
Очень познавательно!!
Не хватает 3D анимации......
То что частицы запутаны-это понятно.
Как все это распутать?? :))
А что если. Ваши рассуждния и расчеты, перенести не на частицы, а на информацию??
12:47 “can only be up or down” if you look at the original experiment then you would see that that actually depends on the strength of the magnetic field. when the magnetic field was weak then it was actually spread normally.